MAT334--2020F > Quiz 1

quiz 1 5101

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xuanzhong:
Find the locus of points for:
$$Re(z^{2}) = 4$$
$$Let z=x+iy$$
$$Re((x+iy)^{2}) = 4$$
$$Re(x^{2}+2ixy-y^{2}) = 4$$
$$x^{2} - y^{2} = 4$$
$$\frac{x^{2}}{4} - \frac{y^{2}}{4} = 1$$
Therefore, the locus of z is a hyperbolic curve with $\frac{x^{2}}{4} - \frac{y^{2}}{4} = 1$